AC Power Analysis
Instantaneous Power
Instantaneous power is the power at any instant of time. Unit : Watts
Instantaneous Power
Part-1 : time independent
Part-2 : time dependent
Average Power
Average power is the average of the instantaneous power over one period
T. Unit : Watts
0
Hence, Average Power
Average Power calculation from phasors
Considering phasor voltage & current:
We recognize the following relationship:
Effective or RMS value
The effective value of a periodic current is the DC current that delivers the
same average power to a resistor as the periodic current.
General formula for effective current/voltage:
Effective current/voltage & Average Power
(sinusoid current)
Apparent Power and Power Factor
Voltage and current in time-domain & phasor-domain:
Average Power:
Apparent Power:
Power Factor:
Unity PF : 𝜃𝑣 = 𝜃𝑖
Lagging PF : 𝜃𝑣 > 𝜃𝑖
Leading PF : 𝜃𝑣 < 𝜃𝑖
Power Factor from Impedances
The power factor angle is equal to the angle of the load impedance if the voltage across
the load is V and the current through is I.
Example problem
Determine the power factor of the entire circuit seen by the source. Also calculate the average
power supplied by the source.
Ans: 0.9734 (leading PF); 125 W
Complex Power, S
Complex power contains all information regarding the power absorbed by a certain load
(resistive/inductive/capacitive).
Q
P
S = P + jQ
P = Real Power
Q = Reactive Power
Real and Reactive Powers
Real power (P) :- Average Power in Watts delivered to a load
Reactive power (Q) :- A measure of the energy exchange between the source and reactive elements (unit : VAR)
Reactive power is not useful to us, unlike real power. It is the power going back and forth between the load and
the source.
Q=0
Q>0
Q<0
for a Resistive Load (unity pf)
for an Inductive Load (lagging pf)
for a Capacitive Load (leading pf)
All in one slide!
Example 11.11
The voltage across a load is 𝑣 𝑡 = 60 cos 𝜔𝑡 − 10° and the current through the element
in the direction of the voltage drop is i 𝑡 = 1.5 cos 𝜔𝑡 + 50° . Find (a) the complex and
apparent powers, (b) the real and reactive powers, and (c) the power factor and the load
impedance.
Solution:
Solution:
Solution:
Practice Problem 11.11
Exercise Problem 11.51
For the entire circuit given in the following figure, find (a) the total power factor, (b) the
average power delivered by the source, (c) complex power, and (d) apparent power.
Ans: (a) 0.9956 (lagging); (b) 31.12 W; (c) 31.12 + j2.932; (d) 31.26 VA